Results 41 to 50 of about 34,901 (303)

Triangle-Free Planar Graphs as Segments Intersection Graphs [PDF]

, 1999
We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross ...
Noy, M., Cobos Gavala, Javier, Dana, J. C., De Castro, Natalia, Márquez Pérez, Alberto, Cobos, F. J., Noy, Marc, Márquez, Alberto, Dana Jiménez, Juan Carlos, Castro Ochoa, Natalia de   +9 more
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Graph sparsification techniques for triangle counting [PDF]

, 2020
The triangle count of a graph is a key metric in graph analysis. Especially for social networks, the triangle count is important to assess connectedness of vertices in the graph.
Hermann, Matthias
core   +1 more source

Packing Triangles in Weighted Graphs [PDF]

SIAM Journal on Discrete Mathematics, 2014
v2: 20 pages, corrected version (from 2013) following referee ...
Chapuy, Guillaume, Devos, Matt, Mcdonald, Jessica, Mohar, Bojan, Scheide, Diego   +4 more
openaire   +2 more sources

THE TYPICAL STRUCTURE OF MAXIMAL TRIANGLE-FREE GRAPHS

Forum of Mathematics, Sigma, 2015
Recently, settling a question of Erdős, Balogh, and Petříčková showed that there are at most $2^{n^{2}/8+o(n^{2})}$$n$-vertex maximal triangle-free graphs, matching the previously known lower bound.
JÓZSEF BALOGH, HONG LIU, ŠÁRKA PETŘÍČKOVÁ, MARYAM SHARIFZADEH   +3 more
doaj   +1 more source

The χ-Boundedness of P2∪P3-Free Graphs

Journal of Mathematics, 2022
In the early 1980s, Gyárfás introduced the concept of the χ-bound with χ-binding functions thereby extending the notion of perfectness. There are a number of challenging conjectures about the χ-bound.
Xiao Wang, Donghan Zhang
doaj   +1 more source

Triangle-degree and triangle-distinct graphs

Discrete Mathematics
Let $G$ be a simple graph and $v$ be a vertex of $G$. The triangle-degree of $v$ in $G$ is the number of triangles that contain $v$. While every graph has at least two vertices with the same degree, there are graphs in which every vertex has a distinct triangle-degree. In this paper, we construct an infinite family of graphs with this property. We also
Zhanar Berikkyzy, Beth Bjorkman, Heather C. Smith Blake, Sogol Jahanbekam, Lauren Keough, Kevin Moss, Danny Rorabaugh, Songling Shan   +7 more
openaire   +3 more sources

Testing first-order properties for subclasses of sparse graphs [PDF]

, 2013
We present a linear-time algorithm for deciding first-order (FO) properties in classes of graphs with bounded expansion, a notion recently introduced by Nešetřil and Ossona de Mendez.
Thomas, Robin, Králʼ, Daniel, Dvořák, Zdeněk   +2 more
core   +1 more source

Sufficient conditions for maximally edge-connected and super-edge-connected graphs

Communications in Combinatorics and Optimization, 2017
Let $G$ be a connected graph with minimum degree $\delta$ and edge-connectivity $\lambda$‎. ‎A graph is‎ ‎maximally edge-connected if $\lambda=\delta$‎, ‎and it is super-edge-connected if every minimum edge-cut is‎ ‎trivial; that is‎, ‎if every ...
Lutz Volkmann, Zhen-Mu Hong
doaj   +1 more source

On (p, 1)-Total Labelling of Some 1-Planar Graphs

Discussiones Mathematicae Graph Theory, 2021
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
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Triangle decompositions of planar graphs

Discussiones Mathematicae Graph Theory, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christina M. Mynhardt, Christopher M. van Bommel   +1 more
openaire   +2 more sources